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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane


Authors: Alexandre Fernandes and Maria Ruas
Journal: Proc. Amer. Math. Soc. 141 (2013), 1125-1133
MSC (2010): Primary 14B05; Secondary 14J17
Published electronically: August 20, 2012
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Abstract: The main goal of this work is to show that if two weighted homogeneous (but not homogeneous) function-germs $ (\mathbb{C}^2,0)\rightarrow (\mathbb{C},0)$ are bi-Lipschitz equivalent, in the sense that these function-germs can be included in a strongly bi-Lipschitz trivial family of weighted homogeneous function-germs, then they are analytically equivalent.


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Additional Information

Alexandre Fernandes
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Av. Mister Hull s/n, Campus do PICI, Bloco 914, CEP: 60.455-760, Fortaleza, CE, Brasil
Email: alexandre.fernandes@ufc.br

Maria Ruas
Affiliation: Instituto de Ciências Matemáticas e Computação, Av. Trabalhador São-carlense 400, Centro Caixa Postal: 668 CEP 13560-970, São Carlos SP, Brasil
Email: maasruas@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11388-7
PII: S 0002-9939(2012)11388-7
Keywords: Bi-Lipschitz, isolated complex singularity
Received by editor(s): February 22, 2011
Received by editor(s) in revised form: June 30, 2011, and August 8, 2011
Published electronically: August 20, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.